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Journal of Hengyang Normal University

Matrix Denotation of Quantum State in Quantum Information

Deng-Yu Zhang, Huawei Li

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Matrix denotation of quantum state is convenient for quantum parallel computation.On the basis of matrix and transformation theory,matrix denotation of pure state,mixed state,entangled state and coherent superposition state are analyzed.The results are good for understanding quantum theory.

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This paper is devoted to such a fundamental problem of quantum computing as quantum parallelism. It is well known that quantum parallelism is the basis of the ability of quantum computer to perform in polynomial time computations performed by classical computers for exponential time. Therefore better understanding of quantum parallelism is important both for theoretical and applied research, cf. e.g. David Deutsch \cite{DD}. We present a realistic interpretation based on recently developed prequantum classical statistical field theory (PCSFT). In the PCSFT-approach to QM quantum states (mixed as well as pure) are labels of special ensembles of classical fields. Thus e.g. a single (!) ``electron in the pure state'' ψψψ can be identified with a special `` electron random field,'' say Φψ(ϕ).Φ_ψ(ϕ).Φψ​(ϕ). Quantum computer operates with such random fields. By one computational step for e.g. a Boolean function f(x1,...,xn)f(x_1,...,x_n)f(x1​,...,xn​) the initial random field Φψ0(ϕ)Φ_{ψ_0}(ϕ)Φψ0​​(ϕ) is transformed into the final random field Φψf(ϕ)Φ_{ψ_f}(ϕ)Φψf​​(ϕ) ``containing all values'' of f.f.f. This is the objective of quantum computer's ability to operate quickly with huge amounts of information -- in fact, with classical random fields.
The quantum pure state and mixed state are the most important quantum states in quantum information.They are the foundation of studying density operator,quantum entanglement and quantum decoherence.The two states' definition and innate differences are given in quantum theory.The observable effect for quantum pure states' mutually phase is the most important characteristics in quantum interfer- ence.The transformation from quantum pure state to mixed state is analyzed through measurement of mechanic quantity (?)_z,(?)_x and (?)_n by quantum mechanics methods.The result shows that the measurement of mechanical quantity is anisotropic in the quantum pure state but for quantum mixed state is isotropic.